Context
Matthew 22:32 should be read within the flow of its chapter and the larger argument of Matthew.
Common Interpretations
Jesus quotes this exact passage in the Gospels when the Sadducees challenge Him about the resurrection, saying God is the God of Abraham, Isaac, and Jacob — the God of the living (Matthew 22:32). He is quoting from a passage about His own pre-incarnate appearance. Read the full passage in your Bible (Judges 6:11-24). Key verses are quoted below. Again the pattern. The Malak Yahweh appears. The text moves seamlessly between calling him "the Angel of the LORD" and "the LORD" as if they are the same person — because they are. And Gideon's response upon realizing who he has spoken to is the same response every person has: he believes he will die because he has seen God face to face. An ordinary angel would never produce this response.
Current Position
No defined position is stated here yet beyond the common interpretations above. As related study develops, this section will be updated where the text warrants a clearer conclusion.